I realy dont know if it will work for you, you say it gets Too dry, but
runs all night to cool? well set the temp higher. You wont cool the
way you want it or add moisture.

Normaly the problem is reversed to much humidity in summer, Then you
need a VS DC [ Did you Hear that Daves Heating ] with low low
speed.

A real slow speed removes more moisture , faster speed less, raise the
speed, but its probably on high, get Plants or a Humidifer.